This PR fixes a bug with caching of some expensive parts of the Khuri-
Makdisi Jacobian implementation. This speeds up constructing the
Jacobian group by approximately 95% on the example below. The speedup
was significant enough that I was able to remove `long test` from all
but one test in the Khuri-Makdisi implementation. Testing the entire
Khuri-Makdisi implementation takes slightly longer now that we are
including more tests, but all the tests I've included finish in under 5
seconds (at least on my machine, if the CI complains we can put back
some of the `long test` markers).

```
K = GF(5)
Kx.<x> = FunctionField(K)
t = polygen(Kx)
F.<y> = Kx.extension(t^3 + (2*x^2 + 3*x + 3)*t^2 + (3*x^2 + x)*t + x^5 +
3*x^4 + 4*x^3 + 4*x^2 + x + 4)
J = F.jacobian(model='km_small')
%time J.group()  # Before: About 1 minute. After: about 3 seconds.
```

The performance increase is similar for `km_medium` and `km_large`.

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies
None

URL: sagemath#40221
Reported by: Vincent Macri
Reviewer(s): Kwankyu Lee

This PR fixes a bug with caching of some expensive parts of the Khuri-
Makdisi Jacobian implementation. This speeds up constructing the
Jacobian group by approximately 95% on the example below. The speedup
was significant enough that I was able to remove `long test` from all
but one test in the Khuri-Makdisi implementation. Testing the entire
Khuri-Makdisi implementation takes slightly longer now that we are
including more tests, but all the tests I've included finish in under 5
seconds (at least on my machine, if the CI complains we can put back
some of the `long test` markers).

```
K = GF(5)
Kx.<x> = FunctionField(K)
t = polygen(Kx)
F.<y> = Kx.extension(t^3 + (2*x^2 + 3*x + 3)*t^2 + (3*x^2 + x)*t + x^5 +
3*x^4 + 4*x^3 + 4*x^2 + x + 4)
J = F.jacobian(model='km_small')
%time J.group()  # Before: About 1 minute. After: about 3 seconds.
```

The performance increase is similar for `km_medium` and `km_large`.

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies
None

URL: sagemath#40221
Reported by: Vincent Macri
Reviewer(s): Kwankyu Lee

sagemathgh-40221: Fix caching in Khuri-Makdisi Jacobian implementation
    
This PR fixes a bug with caching of some expensive parts of the Khuri-
Makdisi Jacobian implementation. This speeds up constructing the
Jacobian group by approximately 95% on the example below. The speedup
was significant enough that I was able to remove `long test` from all
but one test in the Khuri-Makdisi implementation. Testing the entire
Khuri-Makdisi implementation takes slightly longer now that we are
including more tests, but all the tests I've included finish in under 5
seconds (at least on my machine, if the CI complains we can put back
some of the `long test` markers).

```
K = GF(5)
Kx.<x> = FunctionField(K)
t = polygen(Kx)
F.<y> = Kx.extension(t^3 + (2*x^2 + 3*x + 3)*t^2 + (3*x^2 + x)*t + x^5 +
3*x^4 + 4*x^3 + 4*x^2 + x + 4)
J = F.jacobian(model='km_small')
%time J.group()  # Before: About 1 minute. After: about 3 seconds.
```

The performance increase is similar for `km_medium` and `km_large`.

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies
None
    
URL: sagemath#40221
Reported by: Vincent Macri
Reviewer(s): Kwankyu Lee

sagemathgh-40221: Fix caching in Khuri-Makdisi Jacobian implementation
    
This PR fixes a bug with caching of some expensive parts of the Khuri-
Makdisi Jacobian implementation. This speeds up constructing the
Jacobian group by approximately 95% on the example below. The speedup
was significant enough that I was able to remove `long test` from all
but one test in the Khuri-Makdisi implementation. Testing the entire
Khuri-Makdisi implementation takes slightly longer now that we are
including more tests, but all the tests I've included finish in under 5
seconds (at least on my machine, if the CI complains we can put back
some of the `long test` markers).

```
K = GF(5)
Kx.<x> = FunctionField(K)
t = polygen(Kx)
F.<y> = Kx.extension(t^3 + (2*x^2 + 3*x + 3)*t^2 + (3*x^2 + x)*t + x^5 +
3*x^4 + 4*x^3 + 4*x^2 + x + 4)
J = F.jacobian(model='km_small')
%time J.group()  # Before: About 1 minute. After: about 3 seconds.
```

The performance increase is similar for `km_medium` and `km_large`.

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies
None
    
URL: sagemath#40221
Reported by: Vincent Macri
Reviewer(s): Kwankyu Lee